U tdT@s~dZddlZdZGdddZGdddZGdd d Zd d Zdd dZdddZdddZ d ddZ ddZ ddZ dS)!z$ Statistics related stuff in igraph N)FittedPowerLaw Histogram RunningMeanmeanmedian percentilequantile power_law_fitc@s2eZdZdZddZddZddZd d d Zd S) raResult of fitting a power-law to a vector of samples Example: >>> result = power_law_fit([1, 2, 3, 4, 5, 6]) >>> result # doctest:+ELLIPSIS FittedPowerLaw(continuous=False, alpha=2.42..., xmin=3.0, L=-7.54..., D=0.21..., p=0.993...) >>> print(result) # doctest:+ELLIPSIS Fitted power-law distribution on discrete data Exponent (alpha) = 2.42... Cutoff (xmin) = 3.000000 Log-likelihood = -7.54... H0: data was drawn from the fitted distribution KS test statistic = 0.21... p-value = 0.993... H0 could not be rejected at significance level 0.05 >>> result.alpha # doctest:+ELLIPSIS 2.42... >>> result.xmin 3.0 >>> result.continuous False cCs(||_||_||_||_||_||_dSN) continuousxminalphaLDp)selfr r r rrrrJ/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/igraph/statistics.py__init__4s zFittedPowerLaw.__init__cCs&d|jj|j|j|j|j|j|jfS)Nz6%s(continuous=%r, alpha=%r, xmin=%r, L=%r, D=%r, p=%r)) __class____name__r r r rrrrrrr__repr__<szFittedPowerLaw.__repr__cCs |jddS)N皙?) significance)summaryrrrr__str__GszFittedPowerLaw.__str__rcCsddt|jg}|d|d|j|d|j|d|d|j|d|d|d|d|j|d |j|d|j|kr|d |n|d |d |S) aReturns the summary of the power law fit. @param significance: the significance level of the Kolmogorov-Smirnov test used to decide whether the input data could have come from the fitted distribution @return: the summary as a string z(Fitted power-law distribution on %s data)discreter zExponent (alpha) = %fzCutoff (xmin) = %fzLog-likelihood = %fz/H0: data was drawn from the fitted distributionzKS test statistic = %fzp-value = %fz$H0 rejected at significance level %gz1H0 could not be rejected at significance level %g ) boolr appendr r rrrjoin)rrresultrrrrJs*         zFittedPowerLaw.summaryN)r)r __module__ __qualname____doc__rrrrrrrrrs  rc@seZdZdZd!ddZd"ddZed d Zed d Zed dZ eddZ d#ddZ ddZ e Z ddZddZddZd$ddZdd ZdS)%ra4Generic histogram class for real numbers Example: >>> h = Histogram(5) # Initializing, bin width = 5 >>> h << [2,3,2,7,8,5,5,0,7,9] # Adding more items >>> print(h) N = 10, mean +- sd: 4.8000 +- 2.9740 [ 0, 5): **** (4) [ 5, 10): ****** (6) NcCs>t||_d|_d\|_|_t|_||r:||dS)zInitializes the histogram with the given data set. @param bin_width: the bin width of the histogram. @param data: the data set to be used. Must contain real numbers. NNN) float _bin_width_bins_min_maxr _running_meanclearadd_many)rZ bin_widthdatarrrrxs  zHistogram.__init__FcCs*t|jdkrL|sd}n0t||j|j|_|j|j|_dg|_d}|S||jkrt||j|j}|t|jkr||S|sdS|t|jd}|jdg||jt|j|j|_|S|sdStt|j||j}dg||jdd<|j||j8_|jt|j|j|_dS)a-Returns the bin index corresponding to the given number. @param num: the number for which the bin is being sought @param create: whether to create a new bin if no bin exists yet. @return: the index of the bin or C{None} if no bin exists yet and {create} is C{False}.rNr') lenr+intr*r,r-extendmathceil)rnumcreater#binidxZ extra_binsrrr_get_bins2 zHistogram._get_bincCs t|jS)z/Returns the number of elements in the histogram)r2r.rrrrnsz Histogram.ncCs|jjS)z1Returns the mean of the elements in the histogram)r.rrrrrrszHistogram.meancCs|jjS)zGReturns the standard deviation of the elements in the histogram)r.sdrrrrr<sz Histogram.sdcCs|jjS)z5Returns the variance of the elements in the histogram)r.varrrrrr=sz Histogram.varcCs8t|}||d}|j||7<|j||dS)zAdds a single number to the histogram. @param num: the number to be added @param repeat: number of repeated additions TN)r)r:r+r.add)rr7repeatr9rrrr>s z Histogram.addcCsDz t|}Wntk r*t|g}YnX|D]}||q0dS)zpAdds a single number or the elements of an iterable to the histogram. @param data: the data to be addedNiter TypeErrorr>)rr1iteratorxrrrr0s  zHistogram.add_manycCsg|_d\|_|_t|_dS)zClears the collected datar(N)r+r,r-rr.rrrrr/s zHistogram.clearccs2|j}|jD] }|||j|fV||j7}q dS)zGenerator returning the bins of the histogram in increasing order @return: a tuple with the following elements: left bound, right bound, number of elements in the binN)r,r+r*)rrDelemrrrbinss zHistogram.binscKs.ddlm}||||}|j|f|dS)zPlotting supportr)DrawerDirectoryN)Zigraph.drawingrGresolveZdraw)rbackendcontextkwdsrGZdrawerrrr__plot__s zHistogram.__plot__NTc Cs|jdks|jdkrdSt|j|jkr>t|j|jkr>d}nd}tt||jt||j}dt||dd}d||f}|rt|j}|rtt|}||d||d } n||d|d } t| d} d |j|j |j fg} |r| dkr| d | |rR|d 7}| D]*\} } } | || | d| | | fq$n2| D](\} } } | || | d| | fqZn0|r| D] \} } } | || | | fqd | S)aReturns the string representation of the histogram. @param max_width: the maximal width of each line of the string This value may not be obeyed if it is too small. @param show_bars: specify whether the histogram bars should be shown @param show_counts: specify whether the histogram counts should be shown. If both I{show_bars} and I{show_counts} are C{False}, only a general descriptive statistics (number of elements, mean and standard deviation) is shown. NzN = 0z%dz%.3f%r'z [%s, %s): %%s z N = %d, mean +- sd: %.4f +- %.4fzEach * represents %d itemsz (%d)*r)r,r-r3r*maxr2strr+r;rr<r!rFr")r max_widthZ show_barsZ show_countsZ number_formatZ num_length format_stringmaxvalZ maxval_lengthscaler#leftrightZcntrrr to_strings>        "zHistogram.to_stringcCs|Sr )r[rrrrr(szHistogram.__str__)r'N)F)r')rMTT)rr$r%r&rr:propertyr;rr<r=r>r0 __lshift__r/rFrLr[rrrrrrks&  %        8rc@seZdZdZd!ddZd"ddZd d Zd d Zed dZ eddZ eddZ eddZ ddZ ddZeZddZddZddZdd ZdS)#raxRunning mean calculator. This class can be used to calculate the mean of elements from a list, tuple, iterable or any other data source. The mean is calculated on the fly without explicitly summing the values, so it can be used for data sets with arbitrary item count. Also capable of returning the standard deviation (also calculated on the fly) NcCs|dk r<|dks |dks |dkr(td|||nNt||_t||_|dkr~t|dt|d|_t||_n d|_d|_dS)agRunningMean(items=None, n=0.0, mean=0.0, sd=0.0) Initializes the running mean calculator. There are two possible ways to initialize the calculator. First, one can provide an iterable of items; alternatively, one can specify the number of items, the mean and the standard deviation if we want to continue an interrupted calculation. @param items: the items that are used to initialize the running mean calcuator. If C{items} is given, C{n}, C{mean} and C{sd} must be zeros. @param n: the initial number of elements already processed. If this is given, C{items} must be C{None}. @param mean: the initial mean. If this is given, C{items} must be C{None}. @param sd: the initial standard deviation. If this is given, C{items} must be C{None}.Nrz1n, mean and sd must be zeros if items is not Noner'rOr^) ValueErrorr/r0r)_nitems_mean_sqdiff_sd)ritemsr;rr<rrrr7s    zRunningMean.__init__r'cCsxt|}|j|7_||j}|j|||j7_|j||||j7_|jdkrt|j|jdd|_dS)zRunningMean.add(value, repeat=1) Adds the given value to the elements from which we calculate the mean and the standard deviation. @param value: the element to be added @param repeat: number of repeated additions r'?N)r3r`rarbrc)rvaluer?deltarrrr>Zs   zRunningMean.addcCsDz t|}Wntk r*t|g}YnX|D]}||q0dS)aRunningMean.add(values) Adds the values in the given iterable to the elements from which we calculate the mean. Can also accept a single number. The left shift (C{<<}) operator is aliased to this function, so you can use it to add elements as well: >>> rm=RunningMean() >>> rm << [1,2,3,4] >>> rm.result # doctest:+ELLIPSIS (2.5, 1.290994...) @param values: the element(s) to be added @type values: iterableNr@)rvaluesrCrfrrrr0ks  zRunningMean.add_manycCsd\|_|_d\|_|_dS)z#Resets the running mean calculator.)r^r^N)r`rarbrcrrrrr/s zRunningMean.clearcCs |j|jfS)z:Returns the current mean and standard deviation as a tuple)rarcrrrrr#szRunningMean.resultcCs|jS)zReturns the current mean)rarrrrrszRunningMean.meancCs|jS)z&Returns the current standard deviationrcrrrrr<szRunningMean.sdcCs |jdS)zReturns the current variationrOrirrrrr=szRunningMean.varcCsd|jjt|j|j|jfS)Nz%s(n=%r, mean=%r, sd=%r))rrr3r`rarcrrrrrs zRunningMean.__repr__cCsd|j|j|jfS)NzRunning mean (N=%d, %f +- %f))r`rarcrrrrrszRunningMean.__str__cCs t|jSr )r)rarrrr __float__szRunningMean.__float__cCs t|jSr )r3rarrrr__int__szRunningMean.__int__cCs t|jSr )complexrarrrr __complex__szRunningMean.__complex__cCs t|jSr )r3r`rrrr__len__szRunningMean.__len__)Nr^r^r^)r')rr$r%r&rr>r0r/r\r#rr<r=rrr]rjrkrmrnrrrrr,s( #     rcCs t|jS)aReturns the mean of an iterable. Example: >>> mean([1, 4, 7, 11]) 5.75 @param xs: an iterable yielding numbers. @return: the mean of the numbers provided by the iterable. @see: RunningMean() if you also need the variance or the standard deviation )rrxsrrrrs rTcCsX|r t|}tt|d}d|t|krHt||d||dSt||SdS)aHReturns the median of an unsorted or sorted numeric vector. @param xs: the vector itself. @param sort: whether to sort the vector. If you know that the vector is sorted already, pass C{False} here. @return: the median, which will always be a float, even if the vector contained integers originally. rOr'N)sortedr3r2r))rpsortmidrrrrs r2KcCs0t|dr t|dd|D|St||d|S)a(Returns the pth percentile of an unsorted or sorted numeric vector. This is equivalent to calling quantile(xs, p/100.0); see L{quantile} for more details on the calculation. Example: >>> round(percentile([15, 20, 40, 35, 50], 40), 2) 26.0 >>> for perc in percentile([15, 20, 40, 35, 50], (0, 25, 50, 75, 100)): ... print("%.2f" % perc) ... 15.00 17.50 35.00 45.00 50.00 @param xs: the vector itself. @param p: the percentile we are looking for. It may also be a list if you want to calculate multiple quantiles with a single call. The default value calculates the 25th, 50th and 75th percentile. @param sort: whether to sort the vector. If you know that the vector is sorted already, pass C{False} here. @return: the pth percentile, which will always be a float, even if the vector contained integers originally. If p is a list, the result will also be a list containing the percentiles for each item in the list. __iter__css|]}|dVqdS)Y@Nr).0rDrrr szpercentile..ry)hasattrr)rprrrrrrrs rauto{Gz?cCsVddlm}|dks|dkr d}|}|dkr 100}. igraph will try to compensate for the finite sample size if n is small. - C{discrete}: exact maximum likelihood estimation when the input comes from a discrete scale (see Clauset et al among the references). - C{auto}: exact maximum likelihood estimation where the continuous method is used if the input vector contains at least one fractional value and the discrete method is used if the input vector contains integers only. @param p_precision: desired precision of the p-value calculation. The precision ultimately depends on the number of resampling attempts. The number of resampling trials is determined by 0.25 divided by the square of the required precision. For instance, a required precision of 0.01 means that 2500 samples will be drawn. @return: a L{FittedPowerLaw} object. The fitted C{xmin} value and the power-law exponent can be queried from the C{xmin} and C{alpha} properties of the returned object. @newfield ref: Reference @ref: MEJ Newman: Power laws, Pareto distributions and Zipf's law. Contemporary Physics 46, 323-351 (2005) @ref: A Clauset, CR Shalizi, MEJ Newman: Power-law distributions in empirical data. E-print (2007). arXiv:0706.1062 r)_power_law_fitN)r hillrr}zunknown method: %s)r r)Zigraph._igraphrlowerr_r)r1r methodZ p_precisionrZforce_continuousrrrr s,  r g?reg?c Cs|s td|rt|}t|dr,|}d}n |g}d}g}|D]}|dksR|dkrZtdt|t|d}t||t|}}|t|kr||dq>|dkr||dq>|d|||d|||q>|r|d}|S) aReturns the qth quantile of an unsorted or sorted numeric vector. There are a number of different ways to calculate the sample quantile. The method implemented by igraph is the one recommended by NIST. First we calculate a rank n as q(N+1), where N is the number of items in xs, then we split n into its integer component k and decimal component d. If k <= 1, we return the first element; if k >= N, we return the last element, otherwise we return the linear interpolation between xs[k-1] and xs[k] using a factor d. Example: >>> round(quantile([15, 20, 40, 35, 50], 0.4), 2) 26.0 @param xs: the vector itself. @param q: the quantile we are looking for. It may also be a list if you want to calculate multiple quantiles with a single call. The default value calculates the 25th, 50th and 75th percentile. @param sort: whether to sort the vector. If you know that the vector is sorted already, pass C{False} here. @return: the qth quantile, which will always be a float, even if the vector contained integers originally. If q is a list, the result will also be a list containing the quantiles for each item in the list. zxs must not be emptyrxFTrr'zq must be between 0 and 1r)r_rqr|r)r2r3r!) rpqrrqsZ return_singler#r;kdrrrr2s.  (rcCs t|jS)a9Returns the standard deviation of an iterable. Example: >>> sd([1, 4, 7, 11]) #doctest:+ELLIPSIS 4.2720... @param xs: an iterable yielding numbers. @return: the standard deviation of the numbers provided by the iterable. @see: RunningMean() if you also need the mean )rr<rorrrr<js r<cCs t|jS)a.Returns the variance of an iterable. Example: >>> var([1, 4, 8, 11]) #doctest:+ELLIPSIS 19.333333... @param xs: an iterable yielding numbers. @return: the variance of the numbers provided by the iterable. @see: RunningMean() if you also need the mean )rr=rorrrr=zs r=)T)rtT)Nr}r~)rT) r&r5__all__rrrrrrr rr<r=rrrrs VB   " 9 8